Presentation on theme: "Environmental Economics 2"— Presentation transcript:
1Environmental Economics 2 The Travel Cost ModelProf. Anil MarkandyaDepartment of Economics and International Development University of BathEnvironmental Economics 2February,
2The Travel Cost Model (TCM) The typical problem of the travel cost modelBasic assumptionsweak complementarityThe single site modelPoisson, Negative BinomialThe problem of on-site samplingExample with LimdepThe multi-site modelConditional logit modelIndependence of Irrelevant alternatives
3The demand for recreation Objective: how revealed preference data can be used to estimate welfare changes caused by different public programs:- change in the quality of a characteristic of a recreational area (example: decrease in the level of pollution of the water at a beach)- Closure of the site (the access to the beach is forbidden)The TCM is based on REVEALED PREFERENCES
4The origin of the TCMHarold Hotelling (1949) “An Economic Study of the Monetary Valuation of Recreation in the National Parks,” Washington, DC: U.S. Department of the Interior, National Park Service and Recreational Planning Division.In a letter to the US Park Service, Hotelling suggests to use TCM to assess the benefits obtained by visitors of a national park.Intuition behind the TCM:Need to travel to reach a site in order to enjoy itWhen I decide to visit a site I need to pay a cost to reach (and enter) the siteThe cost to reach (and enter) the site and the number of visits to the site allow me to estimate a lower bound of the value of the siteI estimate only use-values (non-use values can be assessed through the Contingent Valuation Method)
5Basic assumptionsThe cost of the travel and of the time spent to reach and stay at the site are a proxi for the value of the recreational experienceUse value is assessed taking into account the number of homogeneous visits to the sites among respondentsHomogeneous => visits last same amount of time; I don’t want to mix 1 day visits with multi-day visits!Visits to only one site; avoid visitors that in one day visit several sites (site A, site B, site C…)=> problem to assess the welfare obtained from site A, from site B and so on
6Weak complementarityI assume that the environmental quality of the site affects the number of visits to the site.I assume that if the number of visits is 0, it remains 0 even if there is a marginal increase in the quality of the site.The weak complementarity assumption allows us to identify how the variation in a public good affects the behaviour of a person.The idea behind the weak complementarity assumption is to link a private and a public good so that if the private good is not consumed, I cannot estimate the public good.The basic idea behind the indirect methods of environmental valuation is to infer the monetary value of a change in the level of environmental services of interest from observed market data on some ordinary commodity.
7The single site modelThe single site model describes the demand for recreation of a person during a season (12 months)The quantity demanded is the number of visitsThe price is the cost per visitr = number of visits during a seasontcr = cost of a visitIntuition: who lives close to the site has a low cost per visit. He should visit the site more often than someone who lives further away.
8What determines the number of visits In equation (1) we assumed that only the cost affects the number of visits. Other elements, such as age of the respondent, income, experience, availability of substitute sites may affects the number of visits:2.tcs = price of trip to substitute site s (I expect a positive sign)y = incomez = vector of socio-demographic characteristics of the respondent (age,experience, etc.)3.B = total trip costA+B = Willingness to payA = consumer surplusA = Access valueThe ‘choke price’ is the minimum priceat which the number of trips falls to zero.The consumer surplus is equal to:4.‘choke price’tcrAtcr0Brr0
9Steps in estimating a single site model Define the site to be valuedDefine the recreation uses and seasonsDevelop a sampling strategySpecify the modelDecide on the treatment of multiple purpose tripsDesign and implement the surveyMeasure trip costEstimate the modelCalculate access value
10Define the site to be valued Single site modelWhat do we mean by “single site”?A riverA lakeA beachA park
11Define the recreation uses and seasons What are the site’s functions? Only one function? Or several functions (beach: fishing, swimming, sailing, etc.)?Ask respondents what is their PRIMARILY purpose to visit the siteIf recreation types are similar we can aggregate observations, otherwise we cannot.when you present your results, motivate why you aggregated data from different recreation typesIt can be useful to use dummy variables to take into account different recreation typesDecide the length of the season for recreation (summer, 12 months?)Decide carefully when to do the interviews
12Develop a sampling strategy On-site sampling Vs off-site samplingOn-site sampling- minimize costs- fast collection of data- ‘choke price’ not identified- it is difficult that respondents remain focused on the interview => keep the questionnaire short- who shall I interview? (a person every 5…)}- the sampling plan is not representative of the population- those who visit the site more often are more likely to be surveyedEconometric problems
13Off-site sampling (mail, telephone) - I survey both visitors and non visitors=> representative of the population- ‘choke price’ is identified- expensive: difficult to intercept users- need to define the area to sample=> maximum day’s drive to reach the site- if you have a registry of users, then use it=> registry of anglers, hunters, etc.
14Specify the modelIdentify the variables you want to use in your model:-age, income, experience with the site and similar sites, leisure, job, education, equipment, starting point, length of the visit, number of visits, etc.- don’t ask too many questions- if on-site, no need of warm-up questions- run focus groups, talk to people at the site, to users- test the questionnaire
15Decide on the treatment of multiple purpose trips Goal: you want to survey daily users whose aim is to visit the siteIf you are interviewing a person that does visit the site, but whose primary goal is not visiting the site (for example, visiting a friend) then you should delete this observation from the analysis
16Design and implement the survey The questionnaire is composed by 4 parts:- introduction- questions on visits to the site (and other substitute sites)- questions on last visit (cost, number of people travelling with, starting point, arrival, length, goal of the visit, etc.)- socio-demographic characteristics of the respondentWhen to survey respondents? Not only on Saturdays and Sundays!
17Measure trip cost - travel cost (return cost) - access fee - equipment cost- cost of time
18Cost of timeThe models to study the demand for recreation are models that study the allocation of time, therefore they are very sensitive on the assumptions on the value of timeSimple models assume it is possible to trade off leisure and work time. However, most people do not have the flexibility to shift time in and out of work in exchange for leisure.
19Solution to the problem of time n = respondentrn = number of trips person n takes to the sitetcn = travel cost and entrance feewn = net wage per hourtn = time person n spends at the site1)= 0 for a respondent that must work a fixed number of hours and cannot trade off leisure with work time;= 1 for a respondent that can decide how many hours to work=> It is important to ask respondents what type of job they have
20Estimate the modelCount models for the demand for recreation (Poisson, negative binomial)- Count models only consider non negative values of the dependent variableThe classic count model is:
21The Poisson model The pdf of the Poisson is: 5. is both the mean and the variance of the distribution. It is the expected value of visits. It is assumed to be explained by the independent variables in the model (age, income, etc.)A log-linear form is useful in order to avoid negative probabilities:6.Parameters in equation (6) are estimated by maximum likelihood:7.Consumer surplus, or access value, for each person in the sample is:8.is the expected number of trips for person n from equation 6
22The negative binomialThe Poisson constrains mean and variance of r be identical: E(rn|znβ)=V(rn|znβ)=λnUsually, in the studies of demand for recreation, the variance is larger than the mean, suggesting overdispersion of the data. As a consequence, the standard error estimated by the Poisson are underestimated => inefficient coefficientsThe negative binomial is an approach for relaxing this constraint (we consider a version of the negative binomial model that is equal to a Poisson model with a gamma distributed error term in the mean):Suppose the conditional mean from a Poisson model is the sum of znβ and an unobserved error term θn that represents unobserved individual preferences or unobserved heterogeneity:E(rn)=exp(znβ+θn)We assume that exp(θn)=vn has a normalized gamma distribution
23The negative binomial model: A test of α=0 is a test of H0 = Poisson model is the correct modelIf you find α>0 then overdispersion exists and the correct model is the negative binomial. Also if α<0 the negative binomial is the correct model. LIMDEP does the test in automaticThe mean of the negative binomial is:The variance of the negative binomial is:
24On-site samplingOn-site random samples are truncated at one trip and oversample more frequent users => estimates from eq. 6 are biasedSolution: Endogenous stratified and truncated PoissonIn the Poisson model the dependent variable is (r-1), rather than r.For the negative binomial model, the correction is more complicated and you need to program into Limdep the maximum likelihood routine:
25Calculate access value In the Poisson model, the access value is given by assessing Sn from eq. 8. The estimate of the access value for person n is given by:If one has estimated a Poisson model using a randomly drawn off-site sample, an estimate of aggregate access value is:where POPoff=total number of people in the relevant geographic marketN=number of surveyed persons
26If one estimates a model with an on-site sample, the aggregate access value is given by: POPon=total number of users in a season => somehow you need to find this numbernj=number of persons in the sample taking j trips to the siteR=largest number of trips taken by a person in the sample
27The multi-site modelThe multi-site model is not based on a “quantity demanded approach”, and describes the demand for recreation as a problem of choice among alternatives.The model used is the random utility model (RUM).Choices are explained by the characteristics of the sites.We assume that respondents choose the sites that give them the highest level of utility.This model allows to analyze the behaviour of economic agents when they are facing a problem of choosing which site to visit even when the alternative sites are many (even 1,000!)
28Estimate of the multi-site model Identify what we want to valuateDefine the population to sampleDefine the choice setDecide the sampling plan (on-site sampling is very troublesome)Specify the modelObtain information about the sitesAnalysis of multi-objective visitsData collection: I need to get information on all sitesEstimate of the cost per visit (to all sites)Model estimatesAccess value estimate
29The random utility model On a given choice occasion, a person considers visiting one of C sites denoted as i=1,2,3,….,C.Each site is assumed to give the person a site utility vi.Utilities are assumed to be a function of the trip cost and site characteristicsThe utility for site i assuming a linear form is:19.tc = trip cost of reaching site iqi is a vector of characteristics of site iei is a random error termSite k is chosen if:20.
30An individual’s utility is: U = max(v0, v1, v2, v3,…,vc)V0 is the level of utility obtained by not visiting any site.To capture differences in participation, respondents’ characteristics are captured as explanatory variables in the no-trip utility function:v0 = α0+α1z+eiz is a vector of characteristics believed to influence a person’s propensity for recreationTo capture differences in preferences for different sites, individual characteristics must be interacted with site characteristics.
31Estimate the model The probability that a person visits site k: Pr(βtctck+ βqqk+ek≥ βtctci+ βqqi+ei for all i є C and ≥ α0+α1z+e0 )If the error terms are IID and follow a type I extreme value distribution, equation (37) is estimated through the conditional logit model:38.Parameters α and β are estimated by maximum likelihood:39.where pr(i) is the logit form from eq (38)rin=1 if individual n visited site i, and =0 otherwiseIn circumstances where individuals are observed taking multiple trips tosites over the season, the same likelihood function is used, with rin nowequal to the number of trips taken to site i by individual n
32The restriction of Indipendence of Irrelevant Alternatives (IIA) This restriction implies that the relative odds of choosing between any two alternatives is independent of changes that may aoccur in other alternatives in the choice set.Model (38) violates the IIA restriction.The Nested Logit model and the Mixed Logit model (or Random Coefficient Logit model, or Random Parameter Logit model) by introducing correlation among the site and no-trip utility error terms allow for more general patterns of substitution in the model and tehrefore relax the IIA restriction.
33Estimate Access ValueSuppose site 1 is closed. I estimate the welfare loss for person n from the closure of site 1 per choice occasion:the negative of the coefficient on trip cost, is a measure of the marginal utility of incomeIf person n did not visit site 1 when it was available, then the welfare loss is equal to zeroNow suppose sites 1 through 5 are closed. I estimate the welfare loss for person n from the closure of sites 1 to 5 per choice occasion:
34Estimate the value of a quality change For a quality change the per choice occasion value for person n is:where q*i is a vector indicating a quality change at some or all of the CsitesThe seasonal value for each individual is the total number of choiceoccasions times the person’s per choice occasion value. The meanseasonal per person value is:=sample mean per choice occasion valueT=total number of choice occasions in the season (number of days in theseason)
35The aggregate seasonal value over the population is: where POP is the population of users and potential users
36Fort Phoenix - New Bedford Beach Off siteTelephone interviewsVisits to Fort Phoenix beach, New Bedford, in 1986.N=499 interviews
37Number of visits (r) to Fort Phoenix beach in 1986 Cumulative Cumulativer Frequency Percent Frequency Percent
38Descriptive statistics x Trips to Fort Phoenix Beach in 1986 (in New Bedford, MA)BEACH if respondent visited any beach in the last year, =2 otherwisepfp if household has a pass tp Fort Phoenix, =0 otherwiseRES if the respondent resides in the Greater New Bedford areaAGE Age of the respondentINC Household income in $10,000 unitsc Round-trip travel costs plus monetary value of time to nearest substitute beachcfp Round-trip travel costs plus monetary value of time to Fort Phoenix Beachc Round-trip travel costs plus monetary value of time to next nearest substitute beach
40WTP for visiting Fort Phoenix From the Poisson model, the welfare that the average person receives from visiting Fort Phoenix are given by:WTP = 3.83/0.47 = $8.153.83 = average number of visits to Fort Phoenix0.47 is the negative of the coefficient of the cost to visit Fort PhoenixUsing the negative binomial:WTP = 3.83/0.53 = $7.22